1) Test& Go doesn't limit the type of visa.
2) If you can show the full payment, not just bookings, It should work. (you may need to show requirement documents upon arrival)
3) Medical certificates and Fit&Fly are different. The requirement is as below a sample from the embassy in DC, the USA.
"2.10 A Medical certificate showing no prohibitive diseases. The certificate shall be valid for no more than three months as indicated in Ministerial Regulation No.14 (B.E. 2535). "
The form is here:
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/Medical-Certificate-Form-For-Non-Immigrant-O-A-Long-Stay-Only.pdf